Question 1

Regression analysis involving one dependent variable and more than one independent variable is known as
A)simple regression.
B)linear regression.
C)multiple regression.
D)none of these.

Accepted Answer

Multiple regression involves analyzing the relationship between one dependent variable and two or more independent variables. Therefore, it is the best choice that fits the given definition. Simple regression involves analyzing the relationship between one dependent variable and one independent variable, while linear regression is a type of regression analysis that assumes a linear relationship between the dependent variable and the independent variable(s).

Question 2

The ___________ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
A)residual
B)coefficient of determination
C)dummy variable
D)interaction variable

Accepted Answer

The coefficient of determination, also known as R-squared, measures the proportion of variance in the dependent variable explained by the regression model. It ranges from 0 to 1, with higher values indicating a better fit. Therefore, option B is the best choice. The residual (A) measures the difference between the actual and predicted values of the dependent variable. Dummy variable (C) and interaction variable (D) are regression techniques used for modeling categorical variables and interaction effects, respectively, and are not directly related to measuring the goodness of fit of the regression model.

Question 3

______________ refers to the degree of correlation among independent variables in a regression model.
A)Multicollinearity
B)Tolerance
C)Rank
D)Confidence level

Accepted Answer

Multicollinearity refers to the degree of correlation among independent variables in a regression model. It can be assessed by examining the variance inflation factor (VIF) of each independent variable. A high VIF indicates high multicollinearity, which can lead to issues with the accuracy and reliability of the regression model's coefficients. Therefore, it is important to identify and address multicollinearity in regression analysis. Tolerance refers to the inverse of VIF and is used to assess multicollinearity as well. Rank refers to the number of non-zero singular values in a matrix and is not directly related to multicollinearity. Confidence level refers to the level of certainty in inferential statistics and is not related to multicollinearity in regression models.

Question 4

A variable used to model the effect of categorical independent variables in a regression model is known as a
A)dependent variable.
B)response.
C)dummy variable.
D)predictor variable.

Accepted Answer

A dummy variable is used to represent the effect of a categorical independent variable in a regression model by assigning a value of 0 or 1 to each category. This allows the model to estimate the effect of each category while controlling for other variables. The other options are not correct because the dependent variable is what the model is trying to predict, the response variable is another term for the dependent variable, and predictor variable is used to refer to any independent variable in the model.

Question 5

__________________ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.
A)Interval estimation
B)Hypothesis testing
C)Statistical inference
D)Point estimation

Accepted Answer

Interval estimation involves using sample data to calculate a range of values (an interval) that is believed to contain the true value of the population parameter. Point estimation involves using sample data to calculate a single value (a point estimate) that is believed to be close to the true value of the population parameter. Hypothesis testing involves making decisions about whether to reject or fail to reject a null hypothesis based on sample data, and statistical inference refers to the process of making conclusions, predictions, or decisions about a larger population based on sample data.

Question 6

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?
A)2.32
B)0.43
C)0.19
D)0.89

Accepted Answer

The coefficient of determination (R-squared) is SSR/SST. 
So, R-squared = 10.03/23.29 = 0.43.

Therefore, the answer is B) 0.43.

Question 7

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below? ​ 
A)The residuals have a increasing variance as the dependent variable increases.
B)The model captures the relationship between the variables accurately.
C)The regression model follows the standard normal probability distribution.
D)The residual distribution is consistently scattered about zero.

Accepted Answer

The answer of The scatter chart below displays the residuals...

Question 8

The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?​ 
A)model is time-invariant.
B)model captures the relationship between the variables accurately.
C)residuals are not independent.
D)residuals are normally distributed.

Accepted Answer

The scatter chart shows patterns in the residuals, indicating that they are not randomly distributed and therefore not independent. This suggests that the model may need further refinement to better capture the relationship between the variables. However, the scatter chart does not provide information on whether the model is time-invariant or whether the residuals are normally distributed.

Question 9

The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as
A)postulation.
B)hypothesis testing.
C)statistical inference.
D)empirical research.

Accepted Answer

The described process is the essence of hypothesis testing, which is a fundamental aspect of statistical inference.

Question 10

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as
A)inductive inference.
B)deductive inference.
C)statistical inference.
D)Bayesian inference.

Accepted Answer

Statistical inference is the process of using sample data to make conclusions about a population. Inductive inference involves making generalizations based on particular observations, while deductive inference involves drawing specific conclusions from general principles. Bayesian inference involves using prior knowledge and updating it based on new evidence. Therefore, statistical inference is the most appropriate choice for this question.

Question 11

________________ is used to test the hypothesis that the values of the regression parameters B₀, B₁, B2, ... B_q are all zero. A)An F test B)A t test C)The least squares method D)Extrapolation

Accepted Answer

An F test is used to test the hypothesis that the regression parameters are all zero. A t test is used to test the hypothesis that a single regression parameter is zero. The least squares method is used to estimate the regression parameters. Extrapolation is the process of using a regression model to predict values outside the range of the data.

Question 12

Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?
A)a multiple regression model
B)quadratic regression model
C)a simple regression model
D)a least squares regression model

Accepted Answer

A quadratic regression model is used to incorporate a squared term of the independent variable in addition to the independent variable itself, allowing for a nonlinear relationship to be modeled. A multiple regression model involves multiple independent variables being used to predict a dependent variable, whereas a simple regression model involves only one independent variable. Least squares regression refers to the method of finding the line of best fit in a regression model.

Question 13

A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called
A)a residual.
B)the coefficient of determination.
C)a dummy variable.
D)interaction.

Accepted Answer

A dummy variable is created for each category of a categorical independent variable to include its effect in the regression model. It takes the value of 0 or 1 depending on whether the observation belongs to that category or not.

Question 14

The coefficient of determination
A)takes values between -1 to +1.
B)is equal to zero for a perfect fit.
C)is equal to negative one for the poorest fit.
D)is used to evaluate the goodness of fit.

Accepted Answer

The coefficient of determination is used to evaluate the goodness of fit, so option D is correct. Option A is incorrect because the coefficient of determination takes values between 0 to 1, not -1 to +1. Option B is incorrect because a perfect fit would result in a coefficient of determination of 1, not 0. Option C is incorrect because the coefficient of determination cannot be negative.

Question 15

The _____________ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.
A)residual
B)tolerance factor
C)confidence level
D)accuracy level

Accepted Answer

Confidence level is the percentage of times the interval estimate will contain the true value of the parameter if the same sample size and sampling technique were used to create the interval estimate repeatedly. It is typically expressed as a percentage, such as 90%, 95%, or 99%.

Question 16

The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the
A)milestone.
B)knot.
C)tipping point.
D)watchpoint.

Accepted Answer

In a piecewise linear regression model, the value of the independent variable at which the relationship with the dependent variable changes is referred to as a knot. Milestones and watchpoints are not commonly used terms in this context, and the tipping point refers to a more general concept of a critical threshold in a relationship, not specifically in a piecewise linear regression model.

Question 17

The degree of correlation among independent variables in a regression model is called
A)multicollinearity.
B)interaction.
C)the coefficient of determination.
D)the sum of squared errors (SSE).

Accepted Answer

Multicollinearity refers to the degree of correlation among independent variables in a regression model. This can cause issues with the interpretation of the coefficients and can affect the accuracy of the model's predictions. Therefore, it is important to assess and address multicollinearity in regression analysis.

Question 18

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​ 
A)The residuals have a constant variance.
B)The model fails to capture the relationship between the variables accurately.
C)The model over predicts the value of the dependent variable for small values and large values of the independent variable.
D)The residuals are normally distributed.

Accepted Answer

The scatter chart shows a pattern in the residuals, indicating that the model fails to accurately capture the relationship between the variables. This is shown by the residuals being spread out and not randomly scattered around the horizontal line at y=0. It is not possible to determine if the residuals have a constant variance or if they are normally distributed based on this scatter chart alone. Additionally, there is no evidence to suggest that the model overpredicts the value of the dependent variable for small or large values of the independent variable.

Question 19

A normally distributed error term with mean of zero would
A)have values that are symmetric about the variance.
B)allow more accurate modeling.
C)yield biased regression estimates.
D)be a hyperbolic curve.

Accepted Answer

A normally distributed error term with mean of zero would allow more accurate modeling because it would have a bell-shaped curve, which is the most common distribution in nature.

Question 20

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​ 
A)The residuals have a constant variance.
B)The model captures the relationship between the variables accurately.
C)The model underpredicts the value of the dependent variable for intermediate values of the independent variable.
D)The residual distribution is not normally distributed.

Accepted Answer

The answer of The scatter chart below displays the residuals...

Quiz 7: Linear Regression

Regression analysis involving one dependent variable and more than one independent variable is known as

The ___________ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.

______________ refers to the degree of correlation among independent variables in a regression model.

A variable used to model the effect of categorical independent variables in a regression model is known as a

__________________ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below? ​

The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?​

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as

________________ is used to test the hypothesis that the values of the regression parameters B0, B1, B2, ... Bq are all zero.

Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?

A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called

The coefficient of determination

The _____________ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the

The degree of correlation among independent variables in a regression model is called

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​

A normally distributed error term with mean of zero would

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below?

The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?

________________ is used to test the hypothesis that the values of the regression parameters B₀, B₁, B2, ... B_q are all zero.

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart?